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The total curvature of the portion of a smooth curve that runs from s = so to s₁ >s can be found by integrating í from S1 t₁ t₁ • Sx/v/ dt, | |\ «- K ds = SK So so to s₁. If the curve has some other parameter, say t, then the total curvature is K = where to and t₁ correspond to so and s₁. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤4r. b. Find the total curvature of the parabola y = v = 10x², – -∞

The total curvature of the portion of a smooth curve that runs from s = so to s₁ >s can be found by integrating í from S1 t₁ t₁ • Sx/v/ dt, | |\ «- K ds = SK So so to s₁. If the curve has some other parameter, say t, then the total curvature is K = where to and t₁ correspond to so and s₁. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤4r. b. Find the total curvature of the parabola y = v = 10x², – -∞

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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The total curvature of the portion of a smooth curve that runs from s = so to s₁ > so can be found by integrating * from t₁ t₁ Sxsdt = Sx|v|dt, so to S₁. S₁ S₁ If the curve has some other parameter, say t, then the total curvature is K = So K ds = where to and t₁ correspond to so and $₁. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤4. b. Find the total curvature of the parabola y = 10x², -∞<x<∞. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤ 4. (Type an exact answer, using à as needed.) b. Find the total curvature of the parabola y = 10x², · -∞<x<∞. The total curvature is. (Type an exact answer, using à as needed.) The total curvature is
Transcribed Image Text:The total curvature of the portion of a smooth curve that runs from s = so to s₁ > so can be found by integrating * from t₁ t₁ Sxsdt = Sx|v|dt, so to S₁. S₁ S₁ If the curve has some other parameter, say t, then the total curvature is K = So K ds = where to and t₁ correspond to so and $₁. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤4. b. Find the total curvature of the parabola y = 10x², -∞<x<∞. a. Find the total curvature of the portion of the helix r(t) = ( cos t)i + ( sin t)j + tk, 0≤t≤ 4. (Type an exact answer, using à as needed.) b. Find the total curvature of the parabola y = 10x², · -∞<x<∞. The total curvature is. (Type an exact answer, using à as needed.) The total curvature is
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